Diffusion Models are Evolutionary Algorithms

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising – as originally introduced in the context of diffusion models – to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps.

Introduction. At least two processes in the biosphere have been recognized as capable of generalizing and driving novelty: evolution, a slow variational process adapting organisms across generations to their environment through natural selection (Darwin, 1959; Dawkins, 2016); and learning, a faster transformational process allowing individuals to acquire knowledge and generalize from subjective experience during their lifetime (Kandel, 2013; Courville et al., 2006; Holland, 2000; Dayan & Abbott, 2001). These processes are intensively studied in distinct domains within artificial intelligence. Relatively recent work has started drawing parallels between the seemingly unrelated processes of evolution and learning (Watson & Levin, 2023; Vanchurin et al., 2022; Levin, 2022; Watson et al., 2022; Kouvaris et al., 2017; Watson & Szathm ́ary, 2016; Watson et al., 2016; Power et al., 2015; Hinton et al., 1987; Baldwin, 2018).

Discussion / Conclusion. By aligning diffusion models with evolutionary processes, we demonstrate that diffusion models are evolutionary algorithms, and evolution can be viewed as a generative process. The Diffusion Evolution process inherently includes mutation, selection, hybridization, and reproductive isolation, indicating that diffusion and evolution are two sides of the same coin. Our Diffusion Evolution algorithm leverages this theoretical connection to improve solution diversity without compromise quality too much compared to standard approaches. By integrating latent space diffusion and accelerated sampling, our method scales to high-dimensional spaces, enabling the training of neural network agents in reinforcement learning environments with exceptionally short training time.